p-adic Geometry Learning Seminar (Spring 2024)

p-adic Geometry Learning Seminar (Spring 2024)
2024-04-15

 Introduction:

This is a learning seminar on Rigid connections. We plan to study a recent work of Esnault--Groechenig (https://arxiv.org/abs/2309.15949) and the Fourier transform algorithm for rigid connections on P1 due to Katz [Kat96] and Arinkin [Ari10]. Please find the attached file for more information.


Organizers:

Koji Shimizu (YMSC) and Daxin Xu (MCM)

 

Time:

Monday 14:30--16:00

 

Venue:

MCM110

 

Tentative Plan:

The main goal of this seminar is to study various results around rigid connections: existence of a Frobenius structure on a rigid connection due to Esnault–Groechenig [EG23], application to Simpson's integral conjecture, and the Fourier transform algorithm for rigid connections on the projective line due to Katz and Arinkin [Ari10].

[Ari10] D. Arinkin, Rigid irregular connections on P1, Compos. Math. 146 (2010)

[EG23] H. Esnault and M. Groechenig, Cristallinity of rigid flat connections revisited, arXiv:2309.15949v2 (2023)

 

Upcoming talks:

Date: April 15

Time: 2:30-4 pm

Venue: MCM 110

Title: Applications to integrality and p-curvature conjectures

Speaker: Jiahong Yu (PKU)


Date: April 22

Time: 2:30-4 pm

Venue: MCM 110

Title: Review of formal connections on a punctured disc

Speaker: Yupeng Wang (PKU)


Date: April 29

Time: 2:30-4 pm

Venue: MCM 110

Title: Review of Fourier transform and local Fourier transform

Speaker: TBC


Date: May 6

Time: 2:30-4 pm

Venue: MCM 110

Title: Fourier transform reserves cohomological rigidity

Speaker: TBC


Date: May 13

Time: 2:30-4 pm

Venue: MCM 110

Title: Rigidity index and rank of the Fourier transform

Speaker: TBC


Date: May 20

Time: 2:30-4 pm

Venue: MCM 110

Title: Proof of main results

Speaker: TBC


Date: March 4

Time: 2:30-4 pm

Venue: MCM 110

Title: Overview of the p-adic geometry learning seminar

Speaker: Daxin Xu (MCM)


Date: March 11

Time: 2:30-4 pm

Venue: MCM 110

Title: Higgs–de Rham flow

Speaker: Mao Sheng (USTC)

 

Date: March 18

Time: 2:30-4 pm

Venue: MCM 110

Title: p-adic topology on W-points of a scheme or stack

Speaker: Junwei Wu (MCM)


Date: March 25

Time: 2:30-4 pm

Venue: MCM 110

Title: Frobenius pullback functor for flat connections

Speaker: Koji Shimizu (YMSC)


Date: April 1

Time: 2:30-4 pm

Venue: MCM 110

Title: Rational F-isocrystal property

Speaker: Chenglong Ma (PKU)


Date: April 8

Time: 2:30-4 pm

Venue: MCM 110

Title: Integral Frobenius structure

Speaker: Zhaofeng Yu (Tsinghua)